Longitudinal-torsional compound ultrasonic vibration polishing method for suppressing mid-frequency error of hard and brittle free-form surface

Abstract

The present application relates to a polishing method for hard and brittle free-form surfaces, in particular to a longitudinal-torsional composite ultrasonic vibration polishing method for suppressing mid-frequency error of hard and brittle free-form surfaces, which solves the technical problem that the existing ultrasonic vibration polishing method cannot suppress mid-frequency error in polishing hard and brittle free-form surfaces. The present application adopts a mechanical polishing method, adds longitudinal-torsional composite ultrasonic vibration to the polishing tool, combines the rotation and feeding movements of the polishing tool with the longitudinal-torsional composite ultrasonic vibration to form a spatially complex coupling polishing track, realizes polishing along the material removal direction with the spatially complex coupling polishing track, and thus realizes longitudinal-torsional composite ultrasonic vibration polishing of hard and brittle free-form surfaces. By changing the amplitude and frequency of the longitudinal-torsional composite ultrasonic vibration, the spatial posture of the time-varying removal function during longitudinal-torsional vibration polishing is changed in real time, so that the removal function of each polishing point is different under the action of the spatially complex coupling polishing track, thereby suppressing mid-frequency error.

Description

TECHNICAL FIELD

[0001] The present application relates to a polishing method for hard and brittle free-form surfaces, in particular to a longitudinal-torsional composite ultrasonic vibration polishing method for suppressing mid-frequency errors of hard and brittle free-form surfaces. BACKGROUND

[0002] High-precision free-form optical elements have become a new trend in the field of optical applications due to their unique advantages of improving system imaging quality, lightweight, and high degree of integration. The manufacturing precision requirements of hard and brittle free-form surfaces for optical systems with high resolution, large numerical aperture, and ultra-small distortion have expanded to the full frequency domain, that is, while achieving nanometer-level precision for low-frequency errors of the surface shape, the mid-high frequency errors must also reach sub-nanometer-level precision. Most of the efficient shaping methods for hard and brittle free-form surfaces with multiple degrees of freedom change are sub-aperture polishing methods. As the principle product of the sub-aperture polishing method, mid-high frequency errors can only be suppressed by adjusting the shape of the removal function, reducing the regularity and pitch of the polishing path, reducing the size of the abrasive grains, and increasing the elastic-plastic removal ratio of the hard and brittle material. The complex polishing path of the free-form surface has high requirements for the dynamic characteristics of the machine tool, and the miniaturization of tool size and process parameters will severely restrict the polishing efficiency, and the commonly used mid-high frequency error suppression method in the shaping polishing is also limited.

[0003] In view of the problems of weakening the spatial texture of the surface of hard and brittle materials, difficulty in suppressing mid-frequency errors, and improving processing efficiency, using ultrasonic vibration polishing for free-form surfaces will be one of the important development directions and research hotspots in the future. At present, the ultrasonic vibration polishing method has shown significant comprehensive advantages in polishing of flat surfaces: improving the machinability of hard and brittle materials, increasing the number and uniformity of effective abrasive grains, prolonging the tool life, improving the polishing efficiency, reducing the spatial frequency of the polishing surface texture, reducing the surface roughness and subsurface damage depth, and has been maturely applied in flat optical elements. However, there is little research on ultrasonic vibration polishing for hard and brittle free-form surfaces, and the ultrasonic vibration polishing method for flat surfaces cannot be applied to free-form surfaces. SUMMARY

[0004] The purpose of the present application is to solve the technical problem that the existing ultrasonic vibration polishing method cannot suppress mid-frequency errors in the polishing of hard and brittle free-form surfaces, and to provide a longitudinal-torsional composite ultrasonic vibration polishing method for suppressing mid-frequency errors of hard and brittle free-form surfaces.

[0005] To achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows:

[0006] A longitudinal-torsional composite ultrasonic vibration polishing method for suppressing mid-frequency errors of hard and brittle free-form surfaces, characterized in that it comprises the following steps:

[0007] Step 1, surface shape detection is performed on the hard and brittle free-form surface to be processed, and polishing removal amount of each polishing point of the hard and brittle free-form surface to be processed is determined according to the surface shape detection result, and amplitude and frequency range of longitudinal-torsional composite ultrasonic vibration attached to the polishing tool are determined; the longitudinal-torsional composite ultrasonic vibration includes longitudinal ultrasonic vibration and torsional ultrasonic vibration of a main shaft;

[0008] Step 2, a feed motion path of the polishing tool is selected;

[0009] Step 3, a longitudinal-torsional vibration polishing time-varying removal function under different amplitudes and frequencies of the longitudinal-torsional composite ultrasonic vibration is determined according to the amplitude and the frequency range of the longitudinal-torsional composite ultrasonic vibration, and the longitudinal-torsional composite ultrasonic vibration is superimposed on the feed motion path of the polishing tool to obtain a spatially complex coupled polishing track;

[0010] Step 4, residence time of the polishing tool at each polishing point of the hard and brittle free-form surface to be processed is respectively calculated according to the longitudinal-torsional vibration polishing time-varying removal function and the polishing removal amount of each polishing point of the hard and brittle free-form surface to be processed;

[0011] Step 5, a mechanical polishing method is adopted to change the amplitude and the frequency of the longitudinal-torsional composite ultrasonic vibration during polishing, so that the polishing tool polishes the hard and brittle free-form surface to be processed according to the spatially complex coupled polishing track and the residence time at each polishing point of the hard and brittle free-form surface to be processed;

[0012] Step 6, surface shape detection is performed on the polished hard and brittle free-form surface to be processed to determine whether the polishing target is reached, if the polishing target is reached, polishing of the hard and brittle free-form surface to be processed is completed, otherwise, the polishing is continued by returning to step 5.

[0013] Further, in step 3, the longitudinal-torsional vibration polishing time-varying removal function is:

[0014] TIF(x,y,t)=TIF(x,y)×f(w,A)

[0015] wherein, TIF(x,y,t) is the longitudinal-torsional vibration polishing time-varying removal function, (x,y) is two-dimensional plane coordinates of the polishing point on the hard and brittle free-form surface to be processed, and t is polishing time;

[0016] TIF(x,y) is a removal function per unit time;

[0017] f(w,A) is a function varying with frequency and amplitude of the longitudinal-torsional composite ultrasonic vibration, w is the frequency of the longitudinal-torsional composite ultrasonic vibration, and A is the amplitude of the longitudinal-torsional composite ultrasonic vibration.

[0018] Further, in step 4, the residence time of the polishing tool on the hard and brittle free-form surface to be processed is calculated by the following formula:

[0019]

[0020] Wherein, h(x, y) is the polishing removal amount of the polishing point of the hard brittle free-form surface to be processed, j = 1, 2, …, m, m is the number of scanning lines in the spatial complex coupling polishing track, i = 1, 2, …, n, n is the number of polishing points in each line in the spatial complex coupling polishing track; T(x, y) is the residence time of the polishing tool at the polishing point of the hard brittle free-form surface to be processed.

[0021] Further, in step 3, the longitudinal torsional vibration polishing time-varying removal function is determined through point test.

[0022] Further, step 1 is specifically:

[0023] 1.1, the surface shape of the hard brittle free-form surface to be processed is detected by using LuphoScan or an interferometer, and the medium frequency error frequency distribution data is extracted through FFT analysis or PSD analysis;

[0024] 1.2, the polishing removal amount of each polishing point of the hard brittle free-form surface to be processed is set according to the surface shape detection result, and the amplitude and frequency range of the longitudinal torsional composite ultrasonic vibration attached to the polishing tool are set according to the medium frequency error frequency distribution data.

[0025] Further, in step 2, the feed motion path of the polishing tool is a raster path, and the scanning line distance is the scanning pitch of the raster path.

[0026] Further, in step 5, the frequency and amplitude of the longitudinal torsional composite ultrasonic vibration are randomly changed within the amplitude and frequency range of the longitudinal torsional composite ultrasonic vibration set in step 1.

[0027] Further, in step 2, the polishing tool is a polishing disc, a polishing wheel or a gas bag tool, and the bearing device is a machine tool or a six-degree-of-freedom robot.

[0028] Compared with the prior art, the present application has the beneficial technical effects as follows:

[0029] 1. The longitudinal torsional composite ultrasonic vibration polishing method for inhibiting medium frequency error of a hard brittle free-form surface provided by the present application adopts a mechanical polishing method, and longitudinal torsional composite ultrasonic vibration is attached to the polishing tool, so that the rotation and feed motion of the polishing tool itself are combined with the longitudinal torsional composite ultrasonic vibration, the longitudinal torsional composite ultrasonic vibration changes the spatial posture of the longitudinal torsional vibration polishing time-varying removal function in real time, and thus the inhibition of the medium frequency error is realized.

[0030] 2. The longitudinal-torsional composite ultrasonic vibration polishing method for suppressing medium frequency error of a hard and brittle free-form surface provided by the application adopts an additional longitudinal-torsional composite ultrasonic vibration mode to exert two-dimensional vibration on the tangent plane of the hard and brittle free-form surface, can adapt to different curvature positions of the hard and brittle free-form surface, realizes point-to-point adhesion, can effectively reduce the polishing force and surface roughness of the hard and brittle free-form surface, and enhances the plastic shear effect in polishing. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 It is a schematic diagram of the principle of the existing mechanical polishing method for a hard and brittle free-form surface.

[0032] Figure 2 It is a schematic diagram of the principle of the method of the embodiment of the application.

[0033] Figure 3 It is a simulation schematic diagram of a traditional mechanical polishing method, and the scanning line distance of the polishing tool feeding motion path is 2 mm, wherein (a) is a three-dimensional topography diagram of the hard and brittle free-form surface after polishing, and (b) is a two-dimensional cross-sectional diagram of the hard and brittle free-form surface after polishing.

[0034] Figure 4 It is a simulation schematic diagram of the method of the embodiment of the application, and the scanning line distance of the polishing tool feeding motion path is 2 mm, wherein (a) is a three-dimensional topography diagram of the hard and brittle free-form surface after polishing, and (b) is a two-dimensional cross-sectional diagram of the hard and brittle free-form surface after polishing.

[0035] Figure 5 It is a frequency domain characteristic peak value diagram obtained through FFT analysis. Figure 3

[0036] It is a frequency domain characteristic peak value diagram obtained through FFT analysis. Figure 6 Figure 4 It is a frequency domain characteristic peak value diagram obtained through FFT analysis. DETAILED DESCRIPTION

[0037] The longitudinal-torsional composite ultrasonic vibration polishing method for suppressing medium frequency error of a hard and brittle free-form surface provided by the application adopts an additional longitudinal-torsional composite ultrasonic vibration mode to exert two-dimensional vibration on the tangent plane of the hard and brittle free-form surface, can adapt to different curvature positions of the hard and brittle free-form surface, realizes point-to-point adhesion, can effectively reduce the polishing force and surface roughness of the hard and brittle free-form surface, and enhances the plastic shear effect in polishing.

[0038] A longitudinal-torsional composite ultrasonic vibration polishing method for suppressing medium frequency error of a hard and brittle free-form surface, characterized in that it comprises the following steps:

[0039] ​Step 1, surface shape detection is performed on the hard-brittle free-form surface to be processed, and the polishing removal amount of each polishing point of the hard-brittle free-form surface to be processed is determined according to the surface shape detection result, and the amplitude and frequency range of the longitudinal-torsional composite ultrasonic vibration attached to the polishing tool are determined. The longitudinal-torsional composite ultrasonic vibration includes longitudinal ultrasonic vibration and torsional ultrasonic vibration. Step 1 is specifically as follows:

[0040] 1.1, surface shape detection is performed on the hard-brittle free-form surface to be processed by using LuphoScan or an interferometer, and the medium frequency error frequency distribution data is extracted by FFT (Fast Fourier Transform) analysis or PSD (Power Spectrum Density) analysis;

[0041] 1.2, the polishing removal amount of each polishing point of the hard-brittle free-form surface to be processed is set according to the surface shape detection result, and the amplitude and frequency range of the longitudinal-torsional composite ultrasonic vibration attached to the polishing tool are set according to the medium frequency error frequency distribution data.

[0042] Step 2, the feed motion path of the polishing tool is selected. In the embodiment, the feed motion path of the polishing tool is a raster path, and the scanning line distance of the raster path is the scanning pitch of the raster path.

[0043] Step 3, the longitudinal-torsional vibration polishing time-varying removal function under different amplitudes and frequencies of the longitudinal-torsional composite ultrasonic vibration is determined by dot test according to the amplitude and frequency range of the longitudinal-torsional composite ultrasonic vibration, and the spatial complex coupling polishing track is obtained by superimposing the longitudinal-torsional composite ultrasonic vibration on the feed motion path of the polishing tool. The spatial complex coupling polishing track is formed by superimposing the longitudinal-torsional composite ultrasonic vibration on the rotation and feed motion of the polishing tool itself. The longitudinal-torsional vibration polishing time-varying removal function is as follows:

[0044] TIF(x,y,t) = TIF(x,y) x f(w,A)

[0045] Wherein, TIF(x,y,t) is the longitudinal-torsional vibration polishing time-varying removal function, (x,y) is the two-dimensional plane coordinates of the polishing point on the hard-brittle free-form surface to be processed, and t is the polishing time;

[0046] TIF(x,y) is the removal function per unit time, which is obtained by dot test;

[0047] f(w,A) is a function varying with the frequency and amplitude of the longitudinal-torsional composite ultrasonic vibration, w is the frequency of the longitudinal-torsional composite ultrasonic vibration, and A is the amplitude of the longitudinal-torsional composite ultrasonic vibration.

[0048] Step 4, the residence time of the polishing tool at each polishing point of the hard-brittle free-form surface to be processed is calculated by the following formula according to the longitudinal-torsional vibration polishing time-varying removal function and the polishing removal amount of each polishing point of the hard-brittle free-form surface to be processed:

[0049]

[0050] wherein h(x, y) is the polishing removal amount of the polishing point of the hard and brittle free-form surface to be processed, j = 1, 2, …, m, m is the number of scanning lines in the spatial complex coupling polishing track, i = 1, 2, …, n, n is the number of polishing points in each line of the spatial complex coupling polishing track; T(x, y) is the dwell time of the polishing tool at the polishing point of the hard and brittle free-form surface to be processed.

[0051] Step 5, using a mechanical polishing method, changing the amplitude and frequency of the longitudinal-torsional composite ultrasonic vibration in the polishing process, so that the polishing tool polishes the hard and brittle free-form surface to be processed according to the spatial complex coupling polishing track and the dwell time at each polishing point of the hard and brittle free-form surface to be processed. Wherein the frequency and amplitude of the longitudinal-torsional composite ultrasonic vibration randomly change within the range of the amplitude and frequency of the longitudinal-torsional composite ultrasonic vibration set in step 1. The length of the dwell time determines the polishing speed of the polishing tool, the longer the dwell time, the slower the polishing speed.

[0052] Step 6, detecting the surface shape of the polished hard and brittle free-form surface to be processed, and judging whether the polishing target is reached. If the polishing target is reached, the polishing of the hard and brittle free-form surface to be processed is completed, otherwise, returning to step 5 to continue polishing.

[0053] In this embodiment, a mechanical polishing method is used, and longitudinal-torsional composite ultrasonic vibration is added to the polishing tool, so that the rotational motion and feeding motion of the polishing tool itself are combined with the longitudinal-torsional composite ultrasonic vibration to form a spatial complex coupling polishing track, and the polishing tool polishes along the material removal direction with the spatial complex coupling polishing track, thereby realizing longitudinal-torsional composite ultrasonic vibration polishing of the hard and brittle free-form surface. By changing the amplitude and frequency of the longitudinal-torsional composite ultrasonic vibration, the spatial pose of the removal function is changed in real time, so that the removal function of each polishing point is different under the action of the spatial complex coupling polishing track, thereby realizing the suppression of the medium frequency error.

[0054] Specifically, this embodiment forms a spatial complex coupling polishing track with a time-varying removal function in the form of longitudinal-torsional composite ultrasonic vibration + rotational motion + feeding motion. With the change of the amplitude and frequency of the longitudinal-torsional composite ultrasonic vibration, the spatial form of the removal function in the spatial complex coupling polishing track changes at any time, and the medium frequency error can be suppressed in the time-varying scanning process of the removal function. When the spatial form of the removal function changes at any time, the removal method is no longer the convolution principle of the traditional mechanical polishing method, so the introduction of the medium frequency error, especially the medium frequency ripple error, can be reduced from the root.

[0055] The present application does not limit the type of polishing tool, which is a polishing disc, a polishing wheel or a bladder tool, and the bearing device is a machine tool or a six-degree-of-freedom robot, which can be attached to longitudinal-torsional composite ultrasonic vibration, especially for hard and brittle free curved surfaces, the polishing tool can adapt to different curvature positions of the hard and brittle free curved surface, realize point-to-point fitting, and thus polish the workpiece. On the other hand, the longitudinal-torsional composite ultrasonic vibration is a two-dimensional vibration applied to the tangent plane of the hard and brittle free curved surface, which can effectively reduce the polishing force and surface roughness, and enhance the plastic shear effect in the polishing process.

[0056] The technical principles and beneficial effects of the present application are further illustrated by comparing and analyzing the traditional mechanical polishing method and the method of the present embodiment.

[0057] In the existing traditional mechanical polishing method, the removal amount of the workpiece material is in the form of convolution:

[0058] R(x,y)=TIF1(x,y)*T1(x,y)

[0059] Wherein, R(x,y) is the polishing removal amount in the traditional mechanical polishing, TIF1(x,y) is the removal function per unit time in the traditional mechanical polishing, and T1(x,y) is the residence time of the polishing tool at the polishing point in the traditional mechanical polishing.

[0060] As shown in Figure 1 , the removal function of the traditional mechanical polishing method is a spatially invariant function, E' is the one-dimensional profile of the removal function TIF1(x,y), and F' is the surface texture after traditional mechanical polishing. It can be seen that under the fixed raster scanning pitch, the traditional mechanical polishing is easy to produce regular wavy mid-frequency errors.

[0061] As shown in Figure 2 , in the present embodiment, the longitudinal-torsional vibration polishing time-varying removal function is a spatially time-varying function, f1(x),…,f n (x) are one-dimensional profiles of the longitudinal-torsional vibration polishing time-varying removal function TIF(x,y,t) at different times, and h(x) is the surface texture after longitudinal-torsional composite ultrasonic vibration polishing. It can be seen that by using the strategy of longitudinal-torsional composite ultrasonic vibration and randomly changing its frequency and amplitude, the hard and brittle free surface to be processed after the superposition of the longitudinal-torsional vibration polishing time-varying removal function becomes a texture with irregular shape and small peak-to-valley value, which can effectively suppress and reduce the mid-frequency error.

[0062] As shown in Figure 3 , Figure 4 , respectively, are the simulation diagrams of the traditional mechanical polishing method and the method of the present embodiment when the scanning line distance of the feed motion path is 2mm, Figure 4In the experiment, the amplitude of the longitudinal-torsional composite ultrasonic vibration is 1 μm, and the frequency is 22 KHz. It can be seen that the PV (peak to valley) and RMS (root mean square) values of the surface after the longitudinal-torsional vibration polishing are reduced, and the surface accuracy is also significantly improved.

[0063] As shown in Figure 5 , Figure 6 , FFT analysis is respectively performed on Figure 3 , Figure 4 , the frequency domain features are extracted, and the characteristic peak values are obtained. When the traditional mechanical polishing method is used, a higher mid-frequency ripple error is introduced on the surface to be processed. When the longitudinal-torsional composite ultrasonic vibration polishing method of the embodiment is used, the characteristic peak value is reduced by 50% compared with the characteristic peak value of the traditional mechanical polishing method, and the periodic mid-frequency ripple error generated by the original fixed grating scanning pitch is significantly suppressed.

[0064] In summary, the present application combines the longitudinal-torsional composite ultrasonic vibration on the basis of the traditional mechanical polishing, can effectively realize the elimination of the mid-frequency ripple error and the improvement of the full-band error, can overcome the defects of the mid-frequency error generated in the existing mechanical polishing method, and has good practicability.

Claims

1. A longitudinal-torsional compound ultrasonic vibration polishing method for suppressing mid-frequency errors in brittle free-form surface, characterized in that, The method comprises the following steps: Step 1, surface shape detection is performed on the hard-brittle free-form surface to be processed, polishing removal amounts of each polishing point of the hard-brittle free-form surface to be processed are determined according to the surface shape detection result, and amplitude and frequency range of longitudinal-torsional composite ultrasonic vibration attached to the polishing tool are determined; the longitudinal-torsional composite ultrasonic vibration comprises longitudinal ultrasonic vibration and torsional ultrasonic vibration of a main shaft; Step 2, a feed motion path of the polishing tool is selected; Step 3, a longitudinal-torsional vibration polishing time-varying removal function under different amplitudes and frequencies of the longitudinal-torsional composite ultrasonic vibration is determined according to the amplitude and frequency range of the longitudinal-torsional composite ultrasonic vibration; meanwhile, the longitudinal-torsional composite ultrasonic vibration is superimposed on the feed motion path of the polishing tool to obtain a spatially complex coupled polishing track; Step 4, residence times of the polishing tool at each polishing point of the hard-brittle free-form surface to be processed are respectively calculated according to the longitudinal-torsional vibration polishing time-varying removal function and the polishing removal amounts of each polishing point of the hard-brittle free-form surface to be processed; Step 5, a mechanical polishing method is adopted to change the amplitude and frequency of the longitudinal-torsional composite ultrasonic vibration during polishing, so that the polishing tool polishes the hard-brittle free-form surface to be processed according to the spatially complex coupled polishing track and the residence times at each polishing point of the hard-brittle free-form surface to be processed; Step 6, surface shape detection is performed on the polished hard-brittle free-form surface to be processed to determine whether the polishing target is reached, if the polishing target is reached, the polishing of the hard-brittle free-form surface to be processed is completed, otherwise, the polishing is continued in Step 5.

2. The longitudinal-torsional composite ultrasonic vibration polishing method for suppressing the frequency error of a hard and brittle free-form surface according to claim 1, characterized in that, In Step 3, the longitudinal-torsional vibration polishing time-varying removal function is: TIF(x,y,t)=TIF(x,y)×f(w,A) wherein, TIF(x,y,t) is the longitudinal-torsional vibration polishing time-varying removal function, (x,y) is two-dimensional plane coordinates of the polishing point on the hard-brittle free-form surface to be processed, and t is polishing time; TIF(x,y) is a removal function per unit time; f(w,A) is a function varying with the frequency and amplitude of the longitudinal-torsional composite ultrasonic vibration, w is the frequency of the longitudinal-torsional composite ultrasonic vibration, and A is the amplitude of the longitudinal-torsional composite ultrasonic vibration.

3. The longitudinal-torsional composite ultrasonic vibration polishing method for suppressing the frequency error of the hard and brittle free-form surface according to claim 2, characterized in that, In Step 4, the residence time of the polishing tool on the hard-brittle free-form surface to be processed is calculated by the following formula: wherein, h(x,y) is the polishing removal amount of the polishing point of the hard-brittle free-form surface to be processed, j=1,2,…,m, m is the number of scanning rows in the spatially complex coupled polishing track, i=1,2,…,n, n is the number of polishing points in each row of the spatially complex coupled polishing track; and T(x,y) is the residence time of the polishing tool at the polishing point of the hard-brittle free-form surface to be processed.

4. The longitudinal-torsional combined ultrasonic vibration polishing method for suppressing mid-frequency error in a hard and brittle free-form surface according to any one of claims 1 to 3, characterized in that, In Step 3, the longitudinal-torsional vibration polishing time-varying removal function is determined by point test.

5. The longitudinal-torsional composite ultrasonic vibration polishing method for suppressing the hard-brittle free-form surface mid-frequency error according to claim 4, wherein Step 1 is specifically: 1.1, surface shape detection is performed on the hard-brittle free-form surface to be processed by using LuphoScan or an interferometer, and medium frequency error frequency distribution data are extracted by FFT analysis or PSD analysis; 1.2, polishing removal amounts of each polishing point of the hard-brittle free-form surface to be processed are set according to the surface shape detection result, and amplitude and frequency range of the longitudinal-torsional composite ultrasonic vibration attached to the polishing tool are set according to the medium frequency error frequency distribution data.

6. The longitudinal-torsional composite ultrasonic vibration polishing method for suppressing the hard-brittle free-form surface mid-frequency error according to claim 5, wherein In step 2, the feed motion path of the polishing tool is a raster path, and the polishing stroke distance is the scan pitch of the raster path.

7. The longitudinal-torsional composite ultrasonic vibration polishing method for suppressing the frequency error of the hard and brittle free-form surface according to claim 6, characterized in that, In step 5, the frequency and amplitude of the longitudinal-torsional composite ultrasonic vibration are randomly changed within the range of the amplitude and frequency of the longitudinal-torsional composite ultrasonic vibration set in step 1.

8. The longitudinal-torsional composite ultrasonic vibration polishing method for suppressing the frequency error of the hard and brittle free-form surface according to claim 7, characterized in that, In step 2, the polishing tool is a polishing disc, a polishing wheel or a bladder tool, and the carrier device is a machine tool or a six-degree-of-freedom robot.

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